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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A274528 Square array read by antidiagonals upwards: T(n,k) = A269526(n+1,k+1) - 1, n>=0, k>=0.

Original entry on oeis.org

0, 1, 2, 2, 3, 1, 3, 0, 4, 5, 4, 1, 5, 0, 3, 5, 6, 2, 1, 7, 4, 6, 7, 0, 4, 8, 2, 9, 7, 4, 8, 3, 0, 6, 5, 10, 8, 5, 3, 6, 1, 7, 4, 11, 12, 9, 10, 6, 2, 4, 5, 8, 3, 13, 7, 10, 11, 7, 8, 5, 9, 2, 6, 14, 15, 13, 11, 8, 12, 9, 10, 13, 3, 14, 15, 16, 6, 17, 12, 9, 13, 10, 2, 3, 7, 15, 8, 5, 11, 14, 6
Offset: 0

Views

Author

Omar E. Pol, Jun 29 2016

Keywords

Comments

This sequence has essentially the same properties as the main sequence A269526, but now involves the nonnegative integers.
This version is important because of the following comment from Allan C. Wechsler, originally contributed to A269526. - N. J. A. Sloane, Jun 30 2016
Sprague-Grundy (Nim) values for a combinatorial game played with two piles of counters. Legal moves consist of removing any positive number of counters from either pile, or removing the same number from both piles, or moving any positive number of counters from the right pile to the left pile. If the Nim-values (as in Sprague-Grundy theory) are written in an array indexed by the number of counters in the two piles, we obtain this array. - Allan C. Wechsler, Jun 29 2016 [corrected by N. J. A. Sloane, Sep 25 2016]
The same sequence arises if we construct a triangle, by reading from left to right in each row, always choosing the smallest nonnegative number which does not produce a duplicate number in any row or diagonal. - N. J. A. Sloane, Jul 02 2016
It appears that the numbers generally appear for the first time in or near the first few rows. - Omar E. Pol, Jul 03 2016

Examples

			The corner of the square array begins:
0,  2,  1,  5,  3,  4,  9, 10, 12,  7, 13, 17,
1,  3,  4,  0,  7,  2,  5, 11, 13, 15,  6,
2,  0,  5,  1,  8,  6,  4,  3, 14, 16,
3,  1,  2,  4,  0,  7,  8,  6, 15,
4,  6,  0,  3,  1,  5,  2, 14,
5,  7,  8,  6,  4,  9,  3,
6,  4,  3,  2,  5, 13,
7,  5,  6,  8, 10,
8, 10,  7,  9,
9, 11, 12,
10, 8,
11,

Links

Crossrefs

Cf. A269526, A274529, A274534, A274650, A274652.
Columns 1, 2, 3, 4 give A001477, A004443, A274615, A274619.

Programs

  • Maple
    # From N. J. A. Sloane, Jul 30 2018, based on Heinz's program in A269526
A:= proc(n, k) option remember; local m, s;
         if n=1 and k=1 then 0
       else s:= {seq(A(i, k), i=1..n-1),
                 seq(A(n, j), j=1..k-1),
                 seq(A(n-t, k-t), t=1..min(n, k)-1),
                 seq(A(n+j, k-j), j=1..k-1)};
            for m from 0 while m in s do od; m
         fi
     end:
[seq(seq(A(1+d-k, k), k=1..d), d=1..12)];
  • Mathematica
    A[n_, k_] := A[n, k] = Module[{m, s}, If[n==1 && k==1, 0, s = Join[Table[ A[i, k], {i, 1, n-1}], Table[A[n, j], {j, 1, k-1}], Table[A[n-t, k-t], {t, 1, Min[n, k] - 1}], Table[A[n+j, k-j], {j, 1, k-1}]]; For[m = 0, MemberQ[s, m], m++]; m]];
Table[A[d-k+1, k], {d, 1, 13}, {k, 1, d}] // Flatten (* Jean-François Alcover, May 03 2019, from Maple *)

A274529 Total number of distinct numbers in the first n antidiagonals of infinite Sudoku-type array A269526.

Original entry on oeis.org

1, 3, 4, 6, 6, 8, 10, 11, 13, 14, 16, 18, 18, 20, 20, 22, 22, 24, 26, 26, 27, 29, 30, 32, 35, 35, 38, 40, 40, 41, 43, 43, 43, 43, 47, 47, 47, 52, 53, 53, 54, 56, 58, 58, 60, 60, 60, 62, 64, 64, 67, 67, 68, 73, 74, 74, 74, 74, 77, 78, 78, 79, 80, 87, 87, 87, 87
Offset: 1

Views

Author

Omar E. Pol, Jun 30 2016

Keywords

Comments

a(n) is also the total number of distinct numbers in the first n antidiagonals of the square array A274528.

Examples

			For n = 3, the first three antidiagonals of the square array A269526 are [1], [3, 2], [2, 4, 3]. The first four positive integers are in the list, so a(3) = 4.

Links

Crossrefs

Cf. A269526, A274528, A274530.
Row lengths of A274534.
A275883 is closely related but a different sequence.

Extensions

More terms from Alois P. Heinz, Jun 30 2016

A273138 Row number in which n appears for the first time in the infinite Sudoku-type array A269526.

Original entry on oeis.org

1, 2, 1, 2, 2, 1, 5, 2, 3, 1, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 2, 1, 2, 2, 1, 2, 3, 2, 3, 2, 1, 3, 2, 1, 2, 1, 3, 4, 3, 4, 3, 2, 1, 6, 5, 4, 2, 1, 2, 3, 5, 2, 3, 1, 3, 1, 6, 1, 3, 1, 6, 5, 1, 1, 5, 4, 3, 2, 1, 2, 3, 2, 1, 2, 5, 6, 10, 8, 7, 4, 3, 2, 1, 6, 5, 4, 3, 5, 4, 4, 2, 7, 5, 4, 2, 2, 4, 2, 4, 3
Offset: 1

Views

Author

Omar E. Pol, Jul 02 2016

Keywords

Comments

It appears that in the square array A269526 the numbers generally appear for the first time in or near the first few rows.

Examples

			Diagram with the first 18 positive integers located in the position where they appear for first time in the square array A269526:
1, 3, -, 6, -, -, 10, 11, 13, -,  -, 18,
2, 4, 5, -, 8, -,  -, 12, 14, 16, -,
-, -, -, -, 9, -,  -,  -, 15, 17,
-, -, -, -, -, -,  -,  -,  -,
-, 7, -, -, -, -,  -,  -,
-, -, -, -, -, -,  -,
-, -, -, -, -, -,
-, -, -, -, -,
-, -, -, -,
-, -, -,
-, -,
-,
...
a(9) = 3 because in the square array A269526 the number 9 appears for the first time in the third row.
a(n) <= 6, for n = 1..80.

Links

Crossrefs

First three rows in the square array A269526 are A274315, A274316, A274317.
Cf. A274529, A273139, A274534.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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